Numerical Solution of Singular Integral Equations: Applications

by Pericles S. Theocaris, Prof.; Chair of Mech. A', Athens Technical Univ., 5 K. Zographou St., Zographou, Athens 624, Greece,

Serial Information: Journal of the Engineering Mechanics Division, 1981, Vol. 107, Issue 5, Pg. 753-771

Document Type: Journal Paper


A large variety of boundary-type problems of mathematical physics are investigated, with the results of the investigation summarized; a table is provided as a user manual to engineers familiar in solving boundary-value problems with the aid of the integral equations technique. The methods for the numerical solution of one-dimensional singular integral equations developed previously by a large number of investigators are exact for integrands which are polynomials of degree up to 2n-1 and not n-1, as it was believed. In general, the Lobatto-type methods of numerical solution of Cauchy-type singular integral equations are shown to be very convenient for the calculations arising in plane elasticity problems. The Gauss-, Radau- and Lobatto-type numerical integration rules are, in general, the best rules to be used for the numerical solution of Cauchy-type singular integral equations.

Subject Headings: Numerical analysis | Numerical methods | Integrals | Integral equations | Domain boundary | Boundary value problem | Polynomials | Elastic analysis

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